Seismic data volumes are three-dimensional images of the subsurface that are computed from seismic recordings for the purpose of locating and characterizing hydrocarbon reservoirs. These images show both geophysical and geological features. A traditional representation of seismic data is based on individual samples or voxels without accounting for larger structures in a direct manner. It has been recognized that a different representation for the seismic data may allow discovery of spatial relationship between neighboring samples, even capture these relations and facilitate operations over spatially related samples.
A first step in this direction may be the generation of a tensor representation for seismic data. One example of computing a seismic tensor to represent the orientation of seismic data is disclosed by Luo et al. (“Computation of Dips and Azimuths with Weighted Structure-Tensor Approach,” Geophysics 71, 2006) who use the structure tensor to the derive dips and azimuths that characterize seismic reflections. Another example is disclosed by Engelsma and Hale (“Painting seismic images in 3D,” SEG Expanded Abstracts 29, 1271-1275, (2010), doi:10.1190/1.3513075) who also use the structure tensor to compute geologic bodies in seismic data.
A second step may be exploitation of the tensors for discovery of spatial relationships within the data. In U.S. Pat. No. 7,953,675, Medioni and Mordohai disclose a method for grouping unorganized data with a known technique called tensor voting. Specifically, they present a form of tensor voting for data of very high dimensionality. Similarly, U.S. Patent Application No. 2009/0060307 by Ghanem and Liang describes another method and system for facilitating a tensor voting scheme that describes the context of particular receiver points defined in multidimensional data by accumulation of local information.
The term tensor voting refers to a method of data discovery that groups data points in a multidimensional space first by congregating points within a local neighborhood into a “tensor” that summarizes the alignment of the points in said neighborhood, i.e., the local trend. In the following “voting” step, these local alignments or trends are integrated to regional trends. Each local tensor broadcasts or radiates its trends to neighboring tensors. Similar local trends reinforce each other and form regional trends, while dissimilar local trends cancel each other. U.S. Patent Application No. 2009/0060307 and U.S. Pat. No. 7,953,675 both disclose specific procedures for performing this voting step. Tensor voting methods have been used to heal gaps in line segments such as blood vessels in x-ray tomographic images or pen strokes in handwriting letter recognition, but tensor methods have apparently not been used to heal seismic-geologic objects such as channels.
A main embodiment of the inventive method disclosed herein is not based on tensor voting, and has application to, among other things, discovery and reconstruction of geological features that are at least partially obscured in the seismic data by noise. Instead, different methods for accumulating information encoded by tensors are used. In addition, novel variations of traditional tensor-voting methods are disclosed.